Method for training a neural network for classifying an unknown signal with respect to known signals

Abstract

The device includes a neural network with an input layer 3, an internal layer 4, and an output layer 5. This network is designed to classify data vectors to classes, the synaptic weights in the network being determined through programming on the basis of specimens whose classes are known. Each class is defined during programming as corresponding to a set of neurons of which each represents a domain which contains a fixed number of specimens. The network includes a number of neurons and synaptic weights which have been determined as a function of the classes thus defined.

We claim: 
     
       1. A method for training a neural network to classify an unknown signal of a known type, comprising the steps of: a) selecting at least one feature from each of a plurality of known signals having at least one feature;   b) determining a difference between the selected at least one feature for every different pair of known signals wherein the differences are represented by a plurality of difference-vectors;   c) selecting a first one of the differences vectors as a current difference-vector and determining the k nearest difference-vectors from said current difference-vector wherein a decision domain is created including a group of k+1 difference-vectors;   d) calculating a distribution probability for the group of difference-vectors in the decision domain;   e) introducing a neuron corresponding to the decision domain into an internal layer of neurons of the neural network;   f) calculating a weight represented by a ij  and a weight represented by b i  for each difference-vector connection between an input layer of neurons and the internal layer based upon the distribution probability of the decision domain; and   g) selecting a next one of the difference-vectors as a new current difference-vector and repeating steps (c) through (g) until the last difference-vector is processed, and   h) inputting a plurality of unknown signal difference-vectors into an input layer of the network and calculating a probability based upon the weighting coefficients a ij  and b i  that the unknown signal difference-vectors lie within one of the decision domains,   whereby the neural network is trained to classify the differences between the unknown signal and the known signals thus indicating the degree of correspondence between the unknown signal and the known signals.   
     
     
       2. The method of claim 1 wherein the step of selecting a first one of the differences vectors as a current difference-vector and determining the k nearest difference-vectors from said current difference-vector wherein a decision domain is created including a group of k+1 difference-vectors in conjunction with the step of repeating steps (c) through (g) until the last difference-vector is processed comprises creating a plurality of decision domains each having the same k+1, fixed number of difference-vectors. 
     
     
       3. The method of claim 1 comprising the step of adding a neuron to an output layer of the neural network wherein each output layer neuron corresponds to a class comprising a group of internal layer neurons. 
     
     
       4. The method of claim 1 wherein the step of calculating a distribution probability for each of the decision domains comprises determining a covariance matrix of the k closest neighbors, a centroid of the distribution and principal axes of an ellipsoid representing each decision domain.   
     
     
       5. The method of claim 4 wherein the weights are represented in the equation   Σ.sub.ij x.sub.i a.sub.ij x.sub.j +Σ.sub.i x.sub.i b.sub.i -c<S     wherein S is a previously determined coefficient that expresses a volume of the decision domain under consideration and a ij , b i  and c are determined through identification between the equation and the relation     L(X)=-(X-μ).sup.T Γ.sup.-1 (X-μ)-1n|Γ|     where μ is the centroid of the distribution, Γ is the covariance matrix of the distribution, X is a vector of coordinates of the unknown signal, L(X) is defined by L(X)<S, and T is a mathematical operator meaning that (X-μ) is a transposed vector.   
     
     
       6. The method of claim 4 further comprising the step of providing data to the neural network by transforming n input terms into n+n(n+1)/2 output terms representing x i , x j  at an input to the neural network and connecting each of the output terms to a corresponding neuron in the input layer of neurons in the neural network. 
     
     
       7. The method of claim 1 wherein the unknown signals are signatures including authentic and forged signatures and the known signals are correct signatures.